What will happen? Another job that requires T3 clearance (post-start)

I am waiting for my T3 secret offered by a DoD Contractor, and investigation is open and pending at 275 days. I’m currently working for a company that has both commercial and defense business. Now, if I was to offered an opportunity to work for the defense side of business, which requires a T3 clearance, what will happen when they request the FSO to start process me for T3 clearance? I know that I will be straight forward with them that I am currently in the process, but will they be able to see in-progress security clearance app? How things would be working out?

I suspect that the best move, for you and your employer, will be to allow the current investigation to play out. Once you are eligible, they can move you to a new position.

On the other hand, your current employer CAN grab your investigation and continue it themselves. They may not know that they can do that OR they may not know HOW to do it.